Fast convolution quadrature based impedance boundary conditions

摘要

We consider an eddy current problem in time-domain relying on impedance boundary conditions on the surface of the conductor(s). We pursue its full discretization comprising (i) a finite element Galerkin discretization by means of lowest order edge elements in space, and (ii) temporal discretization based on Runge–Kutta Convolution Quadrature (CQ) for the resulting Volterra integral equation in time. The final algorithm also involves the fast and oblivious approximation of CQ.For this method we give a comprehensive convergence analysis and establish that the errors of spatial discretization, CQ and of its approximate realization add up to the final error bound.